5=1/4x^2+1

Solution for 5=1/4x^2+1 equation:

5=1/4x^2+1

We move all terms to the left:

5-(1/4x^2+1)=0


Domain of the equation: 4x^2+1)!=0

x∈R


We get rid of parentheses

-1/4x^2-1+5=0

We multiply all the terms by the denominator


-1*4x^2+5*4x^2-1=0

Wy multiply elements

-4x^2+20x^2-1=0

We add all the numbers together, and all the variables

16x^2-1=0

a = 16; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·16·(-1)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*16}=\frac{-8}{32}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*16}=\frac{8}{32}
=1/4
$